In an ultra-relativistic heavy-ion collision, the existence of hot and dense nuclear matter, QGP, has been realized at Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC). The HQs are one of the novel probes [1]}, [2]}, [3]} to study the evolution of QGP. The estimated thermalization time of the HQs is greater than the QGP lifetime, which makes HQs a witness to the entire evolution of QGP. The dynamics of the HQs in QGP are usually studied within the framework of the standard Langevin equation, where the time correlation of noise is the delta function. We have studied the dynamics of HQs in the bath of time-correlated thermal noise within the framework of the Langevin equation, where the time correlation of thermal noise is an exponentially decaying function over a particular time span, \(\tau \) . The drag coefficient is related to the thermal noise through the fluctuation-dissipation theorem. We have observed that the presence of memory slows down the momentum evolution of the HQs in the thermal bath resulting into slowing down of the formation of \(R_{AA}\)  and evolution of transverse momentum broadening.
